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Background and development
Precursors to modern public choice theory include the work of Knut Wicksell, whose 1896 essay, "A New Principle of Just Taxation," argued that the just level of taxation should be determined by means of the benefit principle. In linking taxes to private individuals' willingness to pay for the benefits of public expenditures, Wicksell treated public goods and private goods analogously, conceptualizing the state as an institution through which individuals engage in exchange.

Modern public choice theory emerged in the 1940s and 50s as a response to theories of central planning and market socialism, and in particular to the development of the concept of the social welfare function in welfare economics. '''In contrast to welfare economists, who sought to formulate a welfare function for a society that could be used as a standard of economic efficiency by a government planner, the founding scholars of public choice theory—Kenneth J. Arrow, Anthony Downs, Mancur Olson, and James M. Buchanan and Gordon Tullock—challenged the normative desirability and descriptive accuracy of treating the state as a unitary social welfare-maximizing agent. Instead, they sought to examine the processes of choice, either market-based or political, through which welfare policies and other public goods were produced. '''

'Arrow's Social Choice and Individual Values'' (1951) established a framework for the study of collective decision-making procedures. Arrow examined the conditions under which procedures (i.e. voting rules) for aggregating individual preferences into a society-wide welfare function satisfied a particular set of normative criteria. His famous impossibility theorem established deductively that subject to these minimal criteria, no collective decision procedure could produce a coherent preference ordering but could instead result in preference cycling. In parallel to Arrow's result, Duncan Black inaugurated a program for the unified study of the empirical and normative properties of voting rules, specifying for example, the conditions under which majority rule would produce a stable equilibrium. In a series of papers that culminated in' The Theory of Committees and Elections'' (1958), Black outlined a program of unification toward a more general "Theory of Economic and Political Choices" based on common formal methods, developed underlying concepts of what would become median voter theory, and rediscovered earlier works on voting theory.

In his 1957 book, An Economic Theory of Democracy, Anthony Downs proposed a model of rational action in democracies that attempted to circumvent Arrow's impossibility result. Downs argued that if political parties were understood as vote-maximizing agents, competition for votes amongst parties under conditions of uncertainty would produce social policy that tracked the welfare preferences of the median voter. While Downs may have set out to resolve the Arrow paradox, his "economic theory of democracy" introduced a different paradox into the study of politics: the paradox of voting, in which the negligible influence of any single voter on the result of an election outweighed the costs of participation, thereby rendering voting irrational.

'Mancur Olson's The Logic of Collective Action'' (1963) applied a similar analysis of the dynamics of collective action to the study of behavior in large groups.  Olson argued that in large groups such as labor unions, pressure groups, and the state itself, the negligible nature of an individual's contribution to the final provision of a collective good suggested that absent coercion or some other kind of outside incentive, that good might not be provided at all. Olson's account has been influential in conceptualizing collective action in terms of individual incentives: selective benefits of group membership and individual sanctions for noncompliance. Within public choice, Olson's empirical examples have spurred the study of the effects of interest groups on policymaking.'''

Finally, James Buchanan and Gordon Tullock's coauthored volume, The Calculus of Consent: Logical Foundations of Constitutional Democracy (1962), developed a two-stage model of constitutional and parliamentary choice. In an approach that bears a striking similarity to that of John Rawls in A Theory of Justice (1971), Buchanan and Tullock supposed in the first stage that constitutions (rules, obligations, decision and compliance procedures) were chosen by unanimity rule; in the second stage, citizens would behave as self-interested utility maximizers playing by the "rules of the game" decided in the first stage. Unlike Rawls, however, Buchanan and Tullock suppose that individuals in the constitutional choice stage lack only information about their precise role in a society, but possess full information about the distribution of preferences and resources.

Later work in public choice theory by William A. Niskanen modeled the state as a group of self-interested officials, as in the budget-maximizing model of bureaucracy. Peter Coughlin has formalized probabilistic voting theory as an alternative to median voter theory, which produces Nash equilibria in multidimensional space.

, considered one of the landmarks in public choice. In particular, the preface describes the book as "about the political organization" of a free society. But its methodology, conceptual apparatus, and analytics "are derived, essentially, from the discipline that has as its subject the economic organization of such a society" (1962, p. v). The book focuses on positive-economic analysis as to the development of constitutional democracy but in an ethical context of consent. The consent takes the form of a compensation principle like Pareto efficiency for making a policy change and unanimity or at least no opposition as a point of departure for social choice.

Limitations
Amartya Sen has criticized Buchanan and Tullock's reliance on unanimity as a criterion for collective choice. but argued for the logical inconsistency of the Pareto-principle version of unanimity with even minimal liberty in a social-choice framework. More broadly he qualified its use when other information besides personal utility is given a weight in public judgments.

Buchanan and Tullock themselves outline methodological qualifications of the approach developed in their work The Calculus of Consent (1962), p. 30:
 * [E]ven if the model [with its rational self-interest assumptions] proves to be useful in explaining an important element of politics, it does not imply that all individuals act in accordance with the behavioral assumption made or that any one individual acts in this way at all times ... the theory of collective choice can explain only some undetermined fraction of collective action. However, so long as some part of all individual behavior ... is, in fact, motivated by utility maximization, and so long as the identification of the individual with the group does not extend to the point of making all individual utility functions identical, an economic-individualist model of political activity should be of some positive worth.